LEADER 04607nam 22006975 450 001 996418262403316 005 20210430112340.0 010 $a3-030-46366-4 024 7 $a10.1007/978-3-030-46366-3 035 $a(CKB)4100000011363612 035 $a(DE-He213)978-3-030-46366-3 035 $a(MiAaPQ)EBC6272537 035 $a(Au-PeEL)EBL6272537 035 $a(OCoLC)1181849916 035 $a(PPN)252518888 035 $a(EXLCZ)994100000011363612 100 $a20210430h2020 uy 0 101 0 $aeng 135 $aurnn#008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aAn Invitation to Unbounded Representations of ?-Algebras on Hilbert Space$b[electronic resource] /$fby Konrad Schmüdgen 205 $a1st ed. 2020. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2020. 215 $a1 online resource (XVIII, 381 p. 9 illus.) 225 1 $aGraduate Texts in Mathematics,$x0072-5285 ;$v285 311 $a3-030-46365-6 320 $aIncludes bibliographical references and indexes. 327 $aGeneral Notation -- 1 Prologue: The Algebraic Approach to Quantum Theories -- 2 ?-Algebras -- 3 O*-Algebras -- 4 ?-Representations -- 5 Positive Linear Functionals -- 6 Representations of Tensor Algebras -- 7 Integrable Representations of Commutative ?-Algebras -- 8 The Weyl Algebra and the Canonical Commutation Relation -- 9 Integrable Representations of Enveloping Algebras -- 10 Archimedean Quadratic Modules and Positivstellensätze -- 11 The Operator Relation XX*=F(X*X) -- 12 Induced ?-Representations -- 13 Well-behaved ?-Representations -- 14 Representations on Rigged Spaces and Hilbert C*-modules. A Unbounded Operators on Hilbert Space -- B C*-Algebras and Representations -- C Locally Convex Spaces and Separation of Convex Sets -- References -- Symbol Index -- Subject Index. 330 $aThis textbook provides an introduction to representations of general ?-algebras by unbounded operators on Hilbert space, a topic that naturally arises in quantum mechanics but has so far only been properly treated in advanced monographs aimed at researchers. The book covers both the general theory of unbounded representation theory on Hilbert space as well as representations of important special classes of ?-algebra, such as the Weyl algebra and enveloping algebras associated to unitary representations of Lie groups. A broad scope of topics are treated in book form for the first time, including group graded ?-algebras, the transition probability of states, Archimedean quadratic modules, noncommutative Positivstellensätze, induced representations, well-behaved representations and representations on rigged modules. Making advanced material accessible to graduate students, this book will appeal to students and researchers interested in advanced functional analysis and mathematical physics, and with many exercises it can be used for courses on the representation theory of Lie groups and its application to quantum physics. A rich selection of material and bibliographic notes also make it a valuable reference. 410 0$aGraduate Texts in Mathematics,$x0072-5285 ;$v285 606 $aOperator theory 606 $aMathematical physics 606 $aAssociative rings 606 $aRings (Algebra) 606 $aTopological groups 606 $aLie groups 606 $aOperator Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12139 606 $aMathematical Physics$3https://scigraph.springernature.com/ontologies/product-market-codes/M35000 606 $aAssociative Rings and Algebras$3https://scigraph.springernature.com/ontologies/product-market-codes/M11027 606 $aTopological Groups, Lie Groups$3https://scigraph.springernature.com/ontologies/product-market-codes/M11132 615 0$aOperator theory. 615 0$aMathematical physics. 615 0$aAssociative rings. 615 0$aRings (Algebra). 615 0$aTopological groups. 615 0$aLie groups. 615 14$aOperator Theory. 615 24$aMathematical Physics. 615 24$aAssociative Rings and Algebras. 615 24$aTopological Groups, Lie Groups. 676 $a515.724 700 $aSchmüdgen$b Konrad$4aut$4http://id.loc.gov/vocabulary/relators/aut$058474 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996418262403316 996 $aAn Invitation to Unbounded Representations of ?-Algebras on Hilbert Space$91886618 997 $aUNISA